Numbers & Algebra

Answer : B

Explanation :

(A) Four consecutive even numbers can be written as 2n, 2n + 2, 2n + 4 and 2n + 6,where n is any natural number.
Sum = 2n +(2n + 2) + (2n + 4) + (2n +6) = 8n + 12
= 4(2n + 3) not always divisible by 8.
Thus, (A) is not true.
(B) Four consecutive odd numbers can be written as 2n-1, 2n+ 1, 2n + 3, 2n + 5 where n is a natural number
Sum = (2n-1) + (2n + 1) + (2n + 3) + (2n + 5)
= 8n + 8 = 8(n + 1) divisible by 8
Thus, (B) is true
(C) In product of n consecutive natural numbers atleast one is divisible by n, atleast one by n - 1 ... till 1.
Thus product is atleast divisible by
n * (n - 1) * (n - 2) *1  =  n!.
Thus, (C) is not true.
(D) Take four consecutive odd numbers as 7 x 9 x 11 x 13 which is not divisible by 15.
Thus, (D) is not true.